This week's parsha (Torah reading) is פקודי / Pekudei (Sh'mot / Exodus 38:21-40:38) which discusses the completion of the מִשְׁכַּן / Mishkahn (Tabernacle, or tent of meeting) and ends with the phrase "Moses completed all the work. The cloud / הֶעָנָ֖ן covered the Communion Tent, and G-d's glory / וּכְב֣וֹד filled the Tabernacle. Moses could not come into the Communion Tent, since the cloud had rested on it, and G-d's glory filled the Tabernacle. . . G-d's cloud would then remain on the Tabernacle by day, and fire was in it by night. This was visible to the entire family of Israel, in all their travels."
Note that it says "G-d's cloud."
So what is this cloud?
What about the burning bush which attracted Moses, and from which a voice spoke to Moses?
The burning bush was not G-d either. In Sh'mot / Exodus 3:2 Moses did not "see" G-d at all in the bush — it was an "angel" (messenger) not G-d. The angel did not take on the form of a burning bush either -- "G-d's angel appeared to [Moses] in the heart (or flame) of a fire."
How about the cloud on Mount Sinai, mentioned in תְּרוּמָה / Parsha Terumah (Sh'mot / Exodus 20:18) "Moses entered the mist where the Divine was [revealed]."
G-d was not that cloud either.
Two lines later (Sh'mot / Exodus 20:20) G-d tells Moses "Do not make a representation of anything that is with Me."
In this week's parsha the term we are translating as G-d's glory is וּכְב֣וֹד (and glory). כָּבוֹד means glory or honor and the prefix וּ (vav) which is used to mean "and" or "but." Some translations will use the word "presence" for כְב֣וֹד, but this might mislead a reader into thinking that this is somehow part of G-d (and G-d has no parts). It is rather a way we perceive His presence. Glory is a much closer translation than presence. Glory is the translation used in both the Judaica Press and The Living Torah translations. Glory is more accurate and less open to misinterpretation of some physicality. The word כָּבוֹד / 'kavod" is more commonly translated as "honor" than glory. . . In describing G-d's כָּבוֹד / kavod the The Living Torah states it is:
Either a feeling of holiness (cf. Ramban) or an actual physical glow (Moreh Nevukhim 1:44). In any case, G-d's presence was evident in the Tabernacle (Moreh Nevukhim 1:19).
"The Rambam (Moreh Nevuchim 1:64) explains that the term “Kavod Hashem”, or any use of kavod in reference to G-d, has numerous meanings. For example, when Moshe asks from G-d (Sh'mot / Exodus 33:18) “hareini nah es kevodecha”, he was asking to understand the essence of G-d. Therefore, in that instance, the kavod refers to the essence of G-d. In the case of the mishkan (Tabernacle), he explains that the kavod Hashem was a light created by G-d to delineate the importance of that specific place. Therefore, the kavod Hashem referred to in the above verses meant some type of light that was emanating from the mishkan, seen through the surrounding cloud.
"We see a clear example of this at the revelation at Sinai. The Torah (Sh'mot / Exodus 24:16) relates how the kavod Hashem rested on Har Sinai, with the anan enveloping it for six days. On the seventh day, G-d called out to Moshe to enter into the anan, where he then received the Torah. Taking the Rambam’s (Maimonides) interpretation, this would mean the cloud covered the mountain and the light emanated from within it. . .
"A cloud and light are actually ideal representations as they share a common feature. They both exist within the physical world, able to be seen, yet lack any physicality – nobody can “touch” light or “feel” a cloud. G-d is not physical, so there is no means of physically representing Him. Yet there are times when G-d chooses to reveal Himself to the nation, and the people need a means of identifying G-d’s presence. The choice of these two entities reflects the need for the manifestation to be observable, yet still intangible (there are other instances throughout the Torah where these two are used)."
Most Christians believe that G-d had a body (and that body had a name: Jesus). Thus the concept of a G-d as something physical is an inherent part of Christianity (for most Christians), while the Torah and Judaism completely rejects the concept that G-d is anyone or anything. G-dd is Eternal, above time. He is Infinite, beyond space. He cannot be born, and cannot die. Saying that G-d assumes human form makes G-d small, diminishing both His unity and His divinity. As the Torah says: "G-d is not a man." (Bamidbar / Numbers 23:19).
The Torah tells us G-d is incorporeal (has no physicality) time and time again.
"You did not see any image on the day that G‑d spoke to you at Horeb [Sinai]."-- D’varim / Deuteronomy 4:15.
G-d has no physical manifestation -- He is not a bush, a cloud, or a man. (D'varim) Deuteronomy 4:15 clearly tells us that the Israelites did not see G-d in any form. Ergo G-d was NOT the pillar or the cloud. "You cannot see My Face, for man cannot see Me and live." (Sh'mot / Exodus 33:20).
Sh'mot / Exodus 24:17, told us “the appearance of the glory of HaShem was like a consuming fire on the mountaintop before the eyes of the Children of Israel." Note that it says the appearance of the glory of G-d, not the appearance of G-d.
"But will G-d indeed dwell on the earth? Behold the heaven and the heaven of heavens cannot contain You; much less this temple that I have erected." Melachim Alef / 1 Kings 8:27.
What does it mean when, in this parsha, we are told that the people saw a cloud covering the Mishkahn by day and a light (fire) by night? The Rambam explained that this was a creation by G-d to delineate the importance of that specific place (where the Ark of the Covenant was kept). Therefore, some type of light was emanating from the Mishkahn (Tabernacle). By day the people saw the cloud, and just as we might have an electric light on during the day but can't differentiate between sunlight or the light from a street lamp outside during the day the people did not notice the light during the day. At night (when it was dark) the light was seen (Moreh Nevuchim 1:64).
For more discussion on the concept of G-d's glory in the Mishkhan (and later in the Temple) you might want to read this article from the Mesora website.